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Real-time high-precision autonomous orbit determination of low Earth orbit (LEO) satellites is crucial for achieving high-precision LEO satellite navigation augmentation. This study presents a real-time high-precision undifferenced kinematic POD algorithm. In contrast to traditional orbit determination algorithms, a modular strategy is employed to decompose the orbit determination algorithm. Additionally, considering the error characteristics of LEO satellite observations, the data processing flow of on-board GNSS receivers is simplified. This approach not only ensures the accuracy of orbit determination but also reduces the computational burden, enhances the real-time performance of the algorithm, and facilitates its hardware implementation. The test results indicate that the orbit determination error of the proposed algorithm exhibits no significant systematic differences, with the RMS values of the three-axis pointing all less than 3 cm. The experimental findings validate the effectiveness and correctness of the proposed method.